so sánh 7^2008+1/7^2009+1 với 7^2098+1/7^2010+1 22/08/2021 Bởi Josephine so sánh 7^2008+1/7^2009+1 với 7^2098+1/7^2010+1
Đáp án: $\dfrac{7^{2008} + 1}{7^{2009} +1} > \dfrac{7^{2009} + 1}{7^{2010} +1}$ Giải thích các bước giải: Ta có: $\dfrac{7^{2008} + 1}{7^{2009} +1}$ $= \dfrac{1}{7}. \dfrac{7^{2009} + 7}{7^{2009} +1}$ $= \dfrac{1}{7} . \dfrac{7^{2009} + 1 + 6}{7^{2009} + 1}$ $= \dfrac{1}{7} (1 + \dfrac{6}{7^{2009} +1})$ $\dfrac{7^{2009} + 1}{7^{2010} +1}$ $= \dfrac{1}{7}. \dfrac{7^{2010} + 7}{7^{2010} +1}$ $= \dfrac{1}{7} . \dfrac{7^{2010} + 1 + 6}{7^{2010} + 1}$ $= \dfrac{1}{7} (1 + \dfrac{6}{7^{2010} +1})$ Vì : $ \dfrac{6}{7^{2009} +1} > \dfrac{6}{7^{2010} +1}$ $⇒ \dfrac{7^{2008} + 1}{7^{2009} +1} > \dfrac{7^{2009} + 1}{7^{2010} +1}$ Bình luận
Đáp án: $\dfrac{7^{2008} + 1}{7^{2009} +1} > \dfrac{7^{2009} + 1}{7^{2010} +1}$
Giải thích các bước giải:
Ta có:
$\dfrac{7^{2008} + 1}{7^{2009} +1}$
$= \dfrac{1}{7}. \dfrac{7^{2009} + 7}{7^{2009} +1}$
$= \dfrac{1}{7} . \dfrac{7^{2009} + 1 + 6}{7^{2009} + 1}$
$= \dfrac{1}{7} (1 + \dfrac{6}{7^{2009} +1})$
$\dfrac{7^{2009} + 1}{7^{2010} +1}$
$= \dfrac{1}{7}. \dfrac{7^{2010} + 7}{7^{2010} +1}$
$= \dfrac{1}{7} . \dfrac{7^{2010} + 1 + 6}{7^{2010} + 1}$
$= \dfrac{1}{7} (1 + \dfrac{6}{7^{2010} +1})$
Vì : $ \dfrac{6}{7^{2009} +1} > \dfrac{6}{7^{2010} +1}$
$⇒ \dfrac{7^{2008} + 1}{7^{2009} +1} > \dfrac{7^{2009} + 1}{7^{2010} +1}$